Addendum: Some references:
Kurihara, Akira
On some examples of equations defining Shimura curves and the Mumford uniformization.
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 25 (1979), no. 3, 277--300.
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Reichert, Markus A. Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields. Math. Comp. 46 (1986), no. 174, 637--658.
http://www.math.uga.edu/~pete/Reichert86.pdf
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Gonzàlez Rovira, Josep Equations of hyperelliptic modular curves. Ann. Inst. Fourier (Grenoble) 41 (1991), no. 4, 779--795.
http://www.math.uga.edu/~pete/Gonzalez.pdf
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Noam Elkies, equations for some hyperelliptic modular curves, early 1990's. [So far as I know, these have never been made publicly available, but if you want to know an equation of a modular curve, try emailing Noam Elkies!]
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Elkies, Noam D. Shimura curve computations. Algorithmic number theory (Portland, OR, 1998), 1--47, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998.
http://arxiv.org/abs/math/0005160
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An algorithm which was used to find explicit defining equations for $X_1(N)$, $N$ prime, can be found in
Pete L. Clark, Patrick K. Corn and the UGA VIGRE Number Theory Group, Computation On Elliptic Curves With Complex Multiplication, preprint.
http://math.uga.edu/~pete/TorsCompv6.pdf
This is just a first pass. I probably have encountered something like 10 more papers on this subject, and I wasn't familiar with some of the papers that others have mentioned.
